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When dealing with many-objectives optimization problems, the concepts of Pareto-optimality and Pareto-dominance are often inefficient in modeling and simulating human decision making. This leads to an unpractical size for the set of Pareto-optimal (PO) solutions, and an additional selection criteria among solutions is usually arbitrarily considered. In the paper, different fuzzy-based definitions of optimality and dominated solutions, being nonpreference based, are introduced and tested on analytical test cases, in order to show their validity and nearness to human decision making. Based on this definitions, different subsets of PO solution set can be computed using simple and clear information provided by the decision maker and using a parameter value ranging from zero to one. When the value of the above parameter is zero, the introduced definitions coincide with classical Pareto-optimality and dominance. When the parameter value is increased, different subset of PO solutions can be obtained corresponding to higher degrees of optimality. Index Terms--Design problems with several criteria, fuzzy optimality definition, multiobjective optimization, limitations of Pareto-optimality.

Influence diagrams have been important models for decision problems because of their ability to both model a problem rigorously at its mathematical level and depict its high-level structure graphically. Once the structure and numerical details of an influence diagram have been specified, it can be evaluated to determine the optimal decision policy. However, when evaluating multiple objectives, in the past this determination was based on the assumption that utility functions that commensurate the objectives are available. This paper extends the structure and solution algorithm for influence diagrams to allow for the inclusion of noncommensurate objectives using multiobjective tradeoff analysis instead of utility theory. This eliminates the need to specify any preference information before the influence diagram is solved. The proposed multiobjective-based methodology is also useful for decisionmakers who either do not want to accept the assumptions of utility theory for a particular problem, or are confronted with a problem in which it is neither practical nor viable to construct a utility function. Additionally, this paper establishes the relationship between multiobjective influence diagrams and multiobjective decision trees. This relationship is important because it allows a decisionmaker to utilize the advantages of both representations. An example problem is presented to introduce both the extended multiobjective influence diagram methodology and the relationship linking multiobjective decision trees to multiobjective influence diagrams. Index Terms--Decision trees, influence diagrams, multiple objectives, risk analysis.